Bounding ATE with ITT

We propose the bounds on ATE using intention-to-treat (ITT) estimator when there are compliers/noncompliers in randomized trials. The bounds are given as ITT<ATE<CACE, where compliers’ average treatment effect (CACE) can be computed from ITT and complier ratio. We show that these bounds can be derived from two assumptions: (1) average treatment effect is greater with compliers than noncompliers or CACE>NACE, (2) noncompliers' average treatment effect (NACE) is nonnegative. We give an example of poverty impacts of health insurance, and effects of adverse selection and moral hazard of health insurance.